Question

A box contains a certain number of balls. On each of 60% balls, letter A is marked. On each of 30% balls, letter B is marked and on each of remaining balls, letter C is marked. A ball is drawn from the box at random. Find the probability that the ball drawn is:

1. marked C
2. A or B
3. neither B nor C

Answer 1

A box contains,

60% balls, letter A is marked.

30% balls, letter B is marked.

10% balls, letter C is marked.

i. Total number of all possible outcomes = 100

Number of favourable outcomes = 10

∴ Required Probability = `"Number of favourable outcomes"/"Total number of all possible outcomes"`

= `10/100`

= `1/10`

ii. The probability that the ball drawn is marked A = `"Number of favourable outcomes"/"Total number of all possible outcomes"`

= `60/100`

= `6/10`  ...(1)

The probability that the ball drawn is marked B = `"Number of favourable outcomes"/"Total number of all possible outcomes"`

= `30/100`

= `3/10`  ...(2)

iii. The probability that the ball drawn is neither B nor C

= 1 – [P(B) + P(C)]

= `1 - [3/10 + 1/10]`

= `1 - 4/10`

= `6/10`

= `3/5`